Talk:Negative temperature

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The second sentence of the article goes as follows:

A system with a negative temperature is not colder than absolute zero, but rather it is, in a sense, hotter than infinite temperature (sic).

It is not clear what the "(sic)" at the end is supposed to mean, it doesn't seem to fit.

In written language, the abbreviation (sic) stands for the latin 'sicut'. It is used when for example a quote containing a spelling mistake is an exact copy of the original. By adding the warning '(sic)', the following signal is given to the reader: "Reader, this spelling mistake is not mine, this quote is copied to the letter."

Sometimes the signal '(sic)' is given when the quote is a statement that looks preposterous. Then '(sic)' signals to the reader: "Reader, it may be hard to beleive that this is a true quote, but it really is a verbatim quote.

Here, '(sic)' is used, but here the context does not involve quoting somebody else. Here the '(sic)' just seems to say: "Now isn't that a whopping surprise?"
--Cleon Teunissen | Talk 23:09, 25 July 2005 (UTC)

I've remove the (sic), because this is not being used in the context of a quote. If readers are going to find this implausible, this can be acknowledged in full prose and then elucidated until it is believable. -- Beland 07:09, 14 August 2005 (UTC)
This is a fine compromise. While the statement that there can be temperatures above infinity seems preposterous, the use of (sic) in the origional meaning of 'as it stands' has been diluted, and its use outside of quotations is rare to the point that it adds little information and would merely cause further confusion. Explicitly stating it is far better in every way. Nazlfrag 08:29, 9 November 2007 (UTC)
I don't remember ever hearing that sic could mean "as it stands." Sic generally means "thus," "so," or "in this way." I don't think it is a shortening of sicut (especially since sicut is simply a compound of sic and ut), but even if it is, sicut has a very similar meaning. Sic is (and always has been) inteded as a note by the editor that a given quote or reference is given as it was in the original. In fact, the usage to indicate that something given outside a quote is exact is a dilution of the original meaning. Either way, saying " . . . hotter than infinite temperature, as it stands." is hardly a sensible sentence, anyways. Eebster the Great (talk) 00:22, 29 March 2009 (UTC)

Accuracy and clarity concerns[edit]

Ow...reading this article always makes my brain hurt. The section "Heat and molecular energy distribution" and the other sections seem to be discussing two different notions of negative temperature. The first distinguishes between different infinite temperatures, and the second is an artifact of accounting for different components of kinetic energy separately.

The first type of negative temperature is rather poorly explained, using apparently contradictory language. ("hotter than infinite"?) I'm worried that it's just plain incorrect. In any case, it needs to be explained a lot better.

It should also be explained that in no circumstances should any object or system have a negative kinetic energy, if indeed that's the case.

The cleanup-verify tag isn't exactly right, but you get the idea. I don't have the referenced book handy; if someone who does can check it and see whether or not it supports any of this article, that would be helpful. -- Beland 07:38, 14 August 2005 (UTC)

This isn't well-written, but the content seems correct. I don't have Kittel with me at home, but the context jives with what I remember. Salsb 23:04, August 15, 2005 (UTC)
The article is quite correct, but not very didactical. The "hotter than infinite temperature" remark is technically correct but not very useful. It would be equally correct, and perhaps more helpful, to say, "If a negative temperature system comes into contact with a positive-temperature system, heat will always flow from the negative temperature system to the positive temperature system. In this sense, a system at negative temperature is hotter than any sysetm at positive temperature." 18:40, 25 October 2005 (UTC)

This whole discussion needs to be much clearer. Since we are discussing the states of particles around a nucleus, the discussion needs to unambigously state that the notion of "negative temperature" is more realisically "energies lower than you can get just by cooling things down". If there were an article on "quantum thermodynamics", much of the discussion would go there.

Nothing that I see here is inherently wrong other than the "hotter than infinite". Remember that division by zero is not defined; it does not equal infinity. S Schaffter 22:08, 22 January 2006 (UTC)

Riemann sphere much? Melchoir 01:11, 11 February 2006 (UTC)
I also am bothered by the term "hotter than infinite". In what system? In the same system? Sure, depending on how you define terms. But that's just because there is a bound on the energy of the system (the higher energy, at some point, has a smaller number of states). So it may be best to say that negative temperature is hotter than infinite temperature "for that same system", or some such. - Paul Rimmer, 03 January 2008 —Preceding unsigned comment added by (talk) 16:37, 3 January 2008 (UTC)

Name of article[edit]

Thanks to GregGWood for making the redirect here to fulfill my requested article, negative absolute temperature. It hadn't occurred to me to search under this simpler name.

But I wonder if it's really a very good name. To physicists I suppose "negative temperature" is unambiguous, but to the layman, a temperature below the zero of whatever scale he's used to might be called a negative temperature. There's not even a mention of this linguistic possibility in the lead section. Not that I'm saying there should be (I can't think of a wording that's not just plain ugly), but if the article were at negative absolute temperature (with a redirect from negative temperature) it should head off such a possible confusion. --Trovatore 23:00, 16 March 2006 (UTC)

Hmm... I think "Negative temperature" is okay. If you Google ("negative temperature" -coefficient), I'd estimate only about 10% of hits are talking about subzero temperatures on some scale, so there doesn't seem to be a discrepancy with common usage. Conversely, that search gets 245,000 hits, while inserting "absolute" gets just 252, so "negative temperature" really is the more common name for the concept.
Regardless of its name, what this article could use is an explicit explanation at the top that this article is talking about a qualitative difference in temperature, not a numerical artifact of a scale like Celsius. Melchoir 23:24, 16 March 2006 (UTC)
As long as you can do it without using the words "this article" or similar "metalanguage". I really dislike that. If an article describes the content well enough, it shouldn't have to describe itself. --Trovatore 23:46, 16 March 2006 (UTC)
Indeed. Let's see... Melchoir 23:58, 16 March 2006 (UTC)
Nice job! --Trovatore 00:35, 17 March 2006 (UTC)

new comment[edit]

I'm reverting this article, to see if it has been vandlised--WngLdr34 23:40, 18 November 2006 (UTC)

Sorry, WngLdr34, but I can't make out what you mean. You don't seem to have edited the article. By the way, new comments on talk pages should go to the bottom of the page. Welcome to WP! --Trovatore 22:28, 19 November 2006 (UTC)
To properly check for vandalism, you can examine the difference between any two edits on the history tab without reverting anything. Thanks for looking out for vandals though! Nazlfrag 08:36, 9 November 2007 (UTC)

I think I know what he means: Negative Temperature doesn´t exists. Temperature is only defined in equilibrium states and all the examples just look like Negative Temperature if you just watch a small aspect of the system whitch is not in equilibrium with the rest of the system.

You could try the same complaint about positive temperatures, especially in the theory of heat flow, which relies upon the concept of temperature gradients. A small system does not have to be in equilibrium with "the rest of the system" -- its surroundings -- to have a meaningful temperature. Its internal relaxation time must simply be shorter than its relaxation time due to external heat transfer. This physical, quantitative criterion has been experimentally verified in many nuclear spin systems. They really are sufficiently isolated from their lattices to have their own temperatures, and sometimes these are negative.
Granted, the article doesn't explain all this, but it will when I work up the energy. Melchoir 18:48, 29 November 2006 (UTC)

Possible copyright infridgement[edit]

Unless i am mistaken, the text refers to page number 462 of 'Thermal Physics'. I quote from paragraph "Heat and molecular energy distribution":

As Kittel and Kroemer (p.462) put it, "The temperature scale from cold to hot runs +0 K, . . . , +300 K, . . . , +∞ K, −∞ K, . . . , −300 K, . . . , −0 K."

Looks like it is referring to this (non-public, but commercial) book: (first one mentioned in the references)

Note: I am not experienced regarding contributing to wikipedia, please excuse me if i did something wrong. I will not take action and remove that part of the text myself, please doublecheck my findings. 09:50, 14 December 2006 (UTC)

You're allowed (even encouraged) to quote from reference materials, even if they're copyright. This has nothing to do with Wikipedia per se; it's a general rule. The borderline where citation becomes infringement is fuzzy and ill-defined, but one brief sentence out of a whole book isn't even on the radar screen. See fair use for more info. --Trovatore 17:41, 14 December 2006 (UTC)

new reference[edit]

you all should take a look at this site

it has more stuff about negative temperature, although i don't know how to add references, all i do on wikipedia is suggest things and edit grammar ;) —The preceding unsigned comment was added by (talk) 04:11, 18 February 2007 (UTC).

The link appears broken, I assume this is the correct link:

It contains the Usenet physics FAQ entry for negative temperature and is a great introduction. It would make a useful reference and caters to laymen. Nazlfrag 08:41, 9 November 2007 (UTC)

Ah, the circularity of numbers...[edit]

I liken these superinfinite negative temperatures to such identities as 1 + 2 + 4 + 8 + 16 + 32... = −1 (see Geometric series: a = 1, r = 2, sum = 1/(1 − 2) = −1) (talk) 11:17, 21 August 2008 (UTC)

(... though if you read the article you cite, you will see that the formula is not valid for your example, so your "identity" is a falsehood!) Dbfirs 11:28, 21 August 2008 (UTC)
To be fair, there are valid interpretations at 1 + 2 + 4 + 8 + · · ·, and Divergent geometric series is a more relevant general article to cite. Also note that Euler himself made exactly the same point as; see [1]. Melchoir (talk) 19:26, 21 August 2008 (UTC)

Upper bound[edit]

The articles reads "Since there is no upper bound on momentum of an atom there is no upper bound", however a concept of absolute hot does exist... XApple (talk) 17:40, 13 June 2009 (UTC)

What is going on with enthropy of an isolated system, in which one element has negative temperature?[edit]

Take the energy adder (radio frequency techniques) and the nuclear spins system. The energy adder gives energy to the spins system. Enthropy of spins system decreases; therefore, enthropy of the energy adder increases (whilst the energy adder is outputting energy). Does it mean that this energy adder also has negative temperature? Or the system isn't isolated enough, and enthropy of the energy adder decreases while enthropy somewhere else increases?

It's just confusing: numbers larger than infinity are negative. One more confusing example:

fraction \frac{1}{x}, where x is larger than positive infinity, is smaller, than fraction\frac{1}{\infin}=0.

Wikiwide (talk) 11:08, 20 November 2009 (UTC)

Laser is not a system with negative temperature[edit]

Temperature is defined for systems in thermal equilibrium. A laser with population inversion created and/or maintained by pumping is a system out of equilibrium and the notion of temperature does not apply. The description of population inversion by a Boltzmann factor with negative T is a mere formal similarity and it has nothing to do with negative temperature. Lesche (talk) 21:38, 13 July 2010 (UTC)

Well, there's equilibrium and equilibrium. If you insist on perfect equilibrium, then you can't define any temperatures until the heat death of the universe. My understanding is that the subsystem of excited-versus-unexcited atoms in a laser has its own equilibrium, which is not of course in equilibrium with the translational/vibrational/rotational modes of those atoms, and that that subsystem is indeed at negative temperature. (But I'm not an expert on the topic.) --Trovatore (talk) 21:42, 13 July 2010 (UTC)

Information in this Article is generally out of date[edit] — Preceding unsigned comment added by (talk) 13:33, 4 January 2013 (UTC)

If this isn't a crock of hooey, why doesn't it have any citations?[edit]

This article has been tagged for its complete dearth of citations for nearly four years. It is clear that this is because the concepts within are utterly and complete bullsh!t, but that no one has been brave enough to call it what it is. I'm going to submit this to the Wikipedia authorities for deletion if this situation isn't fixed by the fourth anniversary of this tag. (talk) 02:29, 7 January 2013 (UTC)

The information is not unreferenced. It's true that it doesn't have inline citations, which is arguably a flaw, but if you'll trouble yourself to find the references you'll see that it is all true. (Inline citations are not any better than general references, if you don't bother to look them up.) --Trovatore (talk) 02:34, 7 January 2013 (UTC)
The problem with a lack of inline citations, though, is that we don't know which information in the article applies to which reference or whether the entire article is properly referenced at all. If one wanted to look up more about a specific part of the article in the references, they wouldn't know which one to look at. Someone who is familiar with or has a copy of the references listed really needs to turn them into inline citations. SilverserenC 11:37, 7 January 2013 (UTC)
That's fine and useful. My point stands, though; if people want to write nonsense and give references that don't actually support it, as the IP was suggesting, they can do that just as well with inline cites, if no one actually bothers to look them up anyway. A cursory attempt to do, with the references that already exist in the article, so would convince any reader, not necessarily of correctness, but at least that the article wasn't making stuff up. --Trovatore (talk) 11:50, 7 January 2013 (UTC)
And that's a fair point, Trovatore, because I came across this by hitting "Random Article" (which is how I usually come to articles) and what I read seemed more counterintuitive than quantum physics, which itself can take some getting used to. I still don't understand the article, but I realize that my reaction was formed when I read what appeared to be nonsense combined with a four-year old tag asking for citations. Anyway, I'm glad we all understand now. (talk) 16:45, 7 January 2013 (UTC)

I added two citations to "The Laws of Thermodynamics: A Very Short Introduction by Peter Atkins, Oxford University Press, 2010" which is a very nice and accessible book that discusses this. (Pages 89-95 are on negative temperature with a reference to pages 10-14 in chapter 1 on Boltzmann's distribution where it discusses that beta is the reciprical of temperature.) RJFJR (talk) 17:10, 8 January 2013 (UTC)

Pretty much every sentence expresses an idea in one of these three of the listed sources. Kittel and Kroemer, Atkins, and Ramsey, Norman. It is simply a matter of labeling169.232.131.133 (talk) 23:18, 9 January 2013 (UTC)


"Noninteracting two–level particles Entropy, thermodynamic beta, and temperature as a function of the energy for a system of N noninteracting two–level particles. The simplest example, albeit a rather nonphysical one, is to consider a system of N particles, each of which can take an energy of either +ε or -ε but are otherwise noninteracting."

It is possible to have physical example, if we have N fermions with spin 1/2 and in a huge external field B (Kinetic energy of the particle<< Magnetic energy) then we have the example. kinetic energy of electron is 3/2KT=3/2*1.38^-23T J K−1 Magnetic energy with intrinsic magnetic moment m is m.B=-928.476377 × 10−26 B J·T− So with B=10^8 Tesla (Magnetars are characterized by their extremely powerful magnetic fields, which can reach the order of ten gigateslas.) and T=300 K we have kinetic energy of electron =6.21 ^-21 J Magnetic energy = 9.2847^-11 >> kinetic energy (talk) 22:41, 13 January 2013 (UTC)

I'm a little unclear on why you have posted this here. Does it relate to something you feel should be changed about the article? If not, this is probably not the place to post it. --Trovatore (talk) 22:57, 13 January 2013 (UTC)
Oh wait — the text you started with is existing article text, and you're objecting to the word "nonphysical"? Sure, we can take that out. I don't know why anyone would claim it's nonphysical, magnetars or no. --Trovatore (talk) 23:03, 13 January 2013 (UTC)
Actually, now that I look at it, I think the point of the "nonphysical" was that the particles are noninteracting. Physical particles, I suppose, are going to interact. Is there some reason they wouldn't, near a magnetar? --Trovatore (talk) 23:05, 13 January 2013 (UTC)

New Article[edit]

"Science News" February 9, 2013, Page 10. "Hottest temp is as negative one: New record reached with ultracold gas at high temperature" by Andrew Grant. (It's in the "In the News section".) RJFJR (talk) 20:06, 11 February 2013 (UTC)

found the online link RJFJR (talk) 20:07, 11 February 2013 (UTC)

Negative temperature depends on how entropy is defined[edit]

According to this article, apparently there are two ways to define temperature, and negative temperatures only come out in one version. (These two temperatures are an old concept, dating all the way back to Gibbs). Perhaps this is relevant to this article. The authors of that arxiv paper also claim that the thermodynamics which admits negative temperatures is incomplete somehow ... I'm not sure I'm convinced about that, though. --Nanite (talk) 16:37, 27 August 2013 (UTC)

I've added some disclaimers in the article about the validity of negative temperature in the meanwhile. Hopefully an expert can sort things out

thedoctar (talk) 08:22, 13 June 2014 (UTC)

A recent very readable paper by Frenkel and Warren ( shows the concept of negative temperature is on very solid footing, and that the defnition of entropy employed by Dunkel and Hilbert has some very undesirable properties.--Allard (talk) 16:47, 23 October 2014 (UTC)

  • Well, let's wait till the reviewers evaluate this paper, it's interesting to see that the paper is "conditionally accepted Am J Phys", and I'm sure that Dunkel and Hilbert will comment on it. --Fedor Babkin (talk) 08:37, 25 October 2014 (UTC)

Another very readable recent new article by Swendsen and Yang ( (building on some arguments by Frenkel and Warren but also providing new arguments) shows that the 'inconsistencies' brought forward by Dunkel and Hilbert (DH) are all 1/N and therefore swamped by thermal noise and vanish in the thermodynamic limit and are for sure immeasurable for all the systems sizes so far realised in experiments. They also show that DH volume entropy is inconsistenst with thermodynamics. Becbuilder (talk) 09:25, 5 November 2014 (UTC)


So ... I guess the big question is: What applications do negative temperature materials have? Is there any specific interest in finding more of these materials, or is it just a peculiar property that some materials have? If they have applications in some areas, we should probably add a section to the article where we mention a few of them. —Kri (talk) 14:00, 24 July 2014 (UTC)

See the beautiful article population inversion. The electron shell system there is not at equilibrium though. (talk) 09:01, 6 February 2015 (UTC)

Population inversion[edit]

Since we started with over half the atoms in the spin-down state, this initially drives the system towards a 50/50 mixture, so the entropy is increasing, corresponding to a positive temperature. However, at some point, more than half of the spins are in the spin-up position.

Is this true? See population inversion article, which says this is impossible with just two states, at least in the case of electron energy levels about an atom. Or does that apply here? What is the mechanism of the "radio frequency" methods mentioned in the article? (talk) 09:00, 6 February 2015 (UTC)